Duality respecting representations and compatible complexity measures for gammoids

We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.     

概率语言多属性群决策方法及其在新型智慧城市市民获得感评价中的应用

针对公众参与的语言信息多属性群决策问题，研究了考虑参与者满意度的概率语言多属性群决策方法。首先，根据参与者的语言评价信息确定并规范化概率语言决策矩阵。然后，对大群体进行共识分析，由最大化参与者群体的满意度构建线性规划模型，确定参与者群组的权重；构造正、负理想方案的评价向量，构建多目标规划模型，用拉格朗日乘子法求解属性权重；定义各方案的加权贴近度，并以此对方案进行排序和优选。最后，通过新型智慧城市市民获得感评价案例验证了模型的可行性和有效性。     

QK乘子代数上的Corona定理和Wolff定理

本文给出对数K-Carleson测度的一个新特征,并以此为工具研究Q_K空间的乘子代数M(Q_K),给出乘子代数M(Q_K)的某些特征描述.利用对数K-Carleson测度及Q_K空间的一个新特征,建立乘子代数M(Q_K)上的Corona定理和Wolff定理.     

Boundary-value problem for a class of second-order parameter-dependent dynamic equations on a time scale

In this study, we consider a boundary value problem generated by a second-order dynamic equation on a time scale and boundary conditions depending on the spectral parameter. We give some properties of the solutions and obtain a formulation of the number of eigenvalues of the problem.     

Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling

We investigate a piecewise-deterministic Markov process with a Polish state space, whose deterministic behaviour between random jumps is governed by a finite number of semiflows. We provide tractable conditions ensuring a form of exponential ergodicity and the strong law of large numbers for the chain given by the post-jump locations. Further, we establish a one-to-one correspondence between invariant measures of the chain and those of the continuous-time process. These results enable us to derive the strong law of large numbers for the latter. The studied dynamical system is inspired by certain models of gene expression, which are also discussed here.     

带有积分边值条件的分数阶微分包含解的存在性

本文利用Hausdorff非紧测度、分数阶的微积分理论和Kakutani不动点定理,研究了满足条件z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds的广义Bagley-Torvik型分数阶微分包含cDv1 z(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)解的存在性.其中1 0,a和λ是给定的常数.     

Tighter Constraints of Multiqubit Entanglement

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.     

Densely defined non‐closable curl on carpet‐like metric measure spaces

The paper deals with the possibly degenerate behaviour of the exterior derivative operator defined on 1‐forms on metric measure spaces. The main examples we consider are the non self‐similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. Although topologically one‐dimensional, they may have positive two‐dimensional Lebesgue measure and carry nontrivial 2‐forms. We prove that in this case the curl operator (and therefore also the exterior derivative on 1‐forms) is not closable, and that its adjoint operator has a trivial domain. We also formulate a similar more abstract result. It states that for spaces that are, in a certain way, structurally similar to Sierpinski carpets, the exterior derivative operator taking 1‐forms into 2‐forms cannot be closable if the martingale dimension is larger than one.